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Combining an OpenFOAM\(^{\textregistered }\)-Based Adjoint Solver with RBF Morphing for Shape Optimization Problems on the RBF4AERO Platform

  • E. M. Papoutsis-KiachagiasEmail author
  • K. C. Giannakoglou
  • S. Porziani
  • C. Groth
  • M. E. Biancolini
  • E. Costa
  • M. Andrejašič
Chapter

Abstract

This chapter presents a combination of an OpenFOAM\(^{\textregistered }\)-based continuous adjoint solver and a Radial Basis Function (RBF)-based morpher forming a software suite able to tackle shape optimization problems. The adjoint method provides a fast and accurate way for computing the sensitivity derivatives of the objective functions (here, drag and lift forces) with respect to the design variables. The latter control a group of RBF control points used to deform both the surface and volume mesh of the CFD domain. The use of the RBF-based morpher provides a fast and robust way of handling mesh and geometry deformations with the same tool. The coupling of the above-mentioned tools is used to tackle shape optimization problems in automotive and aerospace engineering. This work was funded by the RBF4AERO “Innovative benchmark technology for aircraft engineering design and efficient design phase optimisation” project funded by the EU 7th Framework Programme (FP7-AAT, 2007-2013) under Grant Agreement No. 605396 and the presented methods are available for use through the RBF4AERO platform (www.rbf4aero.eu).

Nomenclature

RBF

Radial basis functions

SD

Sensitivity derivatives

FD

Finite differences

PDE

Partial differential equation

SI

Surface integrals

FI

Field integrals

E-SI

Enhanced surface integrals

References

  1. 1.
    A. Beckert and H. Wendland. Multivariate interpolation for fluid-structure-interaction problems using radial basis functions. Constructive Approximation, 5(2):125–134, 2011.zbMATHGoogle Scholar
  2. 2.
    M.E. Biancolini. Mesh morphing and smoothing by means of radial basis functions (RBF): A practical example using Fluent and RBF Morph. In Handbook of Research on Computational Science and Engineering: Theory and Practice (2 vol), pages 347–380, 2011.CrossRefGoogle Scholar
  3. 3.
    A. Heft, T. Indinger, and N. Adams. Experimental and numerical investigation of the DrivAer model. In ASME 2012, Symposium on Issues and Perspectives in Automotive Flows, pages 41–51, Puerto Rico, USA, 8-12 July 2012.Google Scholar
  4. 4.
    I.S Kavvadias, E.M. Papoutsis-Kiachagias, and K.C. Giannakoglou. On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization. Journal of Computational Physics, 301:1–18, 2015.MathSciNetCrossRefGoogle Scholar
  5. 5.
    C. Micchelli. Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constructive Approximation, 2(1):11–22, 1986.MathSciNetCrossRefGoogle Scholar
  6. 6.
    D.I. Papadimitriou and K.C. Giannakoglou. A continuous adjoint method with objective function derivatives based on boundary integrals for inviscid and viscous flows. Journal of Computers & Fluids, 36(2):325–341, 2007.CrossRefGoogle Scholar
  7. 7.
    E.M. Papoutsis-Kiachagias and K.C. Giannakoglou. Continuous adjoint methods for turbulent flows, applied to shape and topology optimization: Industrial applications. Archives of Computational Methods in Engineering, 23(2):255–299, 2016.MathSciNetCrossRefGoogle Scholar
  8. 8.
    A.S. Zymaris, D.I. Papadimitriou, K.C. Giannakoglou, and C. Othmer. Continuous adjoint approach to the Spalart-Allmaras turbulence model for incompressible flows. Computers & Fluids, 38(8):1528–1538, 2009.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • E. M. Papoutsis-Kiachagias
    • 1
    Email author
  • K. C. Giannakoglou
    • 1
  • S. Porziani
    • 2
  • C. Groth
    • 3
  • M. E. Biancolini
    • 3
  • E. Costa
    • 2
  • M. Andrejašič
    • 4
  1. 1.Parallel CFD & Optimization UnitNational Technical University of Athens (NTUA)AthensGreece
  2. 2.D’Appolonia S.p.A.RomeItaly
  3. 3.University of Rome Tor Vergata (UTV)RomeItaly
  4. 4.PIPISTREL d.o.o. Ajdovščina, R&D, Department of AerodynamicsAjdovščinaSlovenia

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